Parameter Estimation, Model Reduction and Quantum Filtering

TL;DR

This dissertation advances quantum filtering by developing parameter estimation methods, model reduction techniques, and applying them to quantum magnetometry and error correction, demonstrating improved estimation accuracy and control strategies.

Contribution

It introduces the quantum particle filter for parameter estimation, applies it to magnetometry, and develops an efficient feedback controller for quantum error correction.

Findings

Quantum particle filter effectively estimates parameters in quantum systems.

Enhanced magnetometry precision through continuous measurement techniques.

Efficient feedback control improves quantum error correction performance.

Abstract

This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimator's uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback controller for continuous-time quantum error correction. Chapter 7 presents an exact model of symmetric processes of collective qubit systems.